Detailed Description

Solver for symmetric band positive definite matrices.

Note: Although the ppbsv solver supports KLU, a zero (half) bandwidth would lead to unwanted warning message from ScaLAPACK.; See: https://github.com/Reference-ScaLAPACK/scalapack/issues/116

It solves the system of linear equations A*X=B with a symmetric band positive definite matrix A. The band matrix A has KLU sub-diagonals. It shall be stored in the following format. The band storage scheme is illustrated by the following example, when M=N=6, KLU=2.

For ‘UPLO='L’`, the lower half is stored.

a11  a22  a33  a44  a55  a66
a21  a32  a43  a54  a65   .
a31  a42  a53  a64   .    .

The lead dimension should be KLU+1.

With zero based indexing, for a general band matrix A, the element at row i and column j is stored at A[IDX(i, j)].

const auto IDX = [&](int i, int j) {
    if(i < j) std::swap(i, j);
    if(i - j > KLU) return -1;
    return i + j * KLU;
};

For ‘UPLO='U’`, the upper half is stored.

 .    .   a13  a24  a35  a46
 .   a12  a23  a34  a45  a56
a11  a22  a33  a44  a55  a66

The lead dimension should be KLU+1.

With zero based indexing, for a general band matrix A, the element at row i and column j is stored at A[IDX(i, j)].

const auto IDX = [&](int i, int j) {
    if(i > j) std::swap(i, j);
    if(j - i > KLU) return -1;
    return 2 * j - i + (j + 1) * KLU;
};

Author: tlc

Date: 07/03/2025

Version: 1.0.0

The documentation for this class was generated from the following file:

ezp/ppbsv.hpp